Clusters and recurrence in the two-dimensional zero-temperature stochastic Ising model

• 成果类型: Article
• 署名作者: Camia, F; De Santis, E; Newman, CM
• 署名单位: New York University; Sapienza University Rome; New York University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• 发表日期: 2002
• 页码: 565-580
• 关键词: dynamics; exponents

摘要

We analyze clustering and (local) recurrence of a standard Markov process model of spatial domain coarsening. The continuous time process, whose state space consists of assignments of +1 or -1 to each site in Z(2), is the zero-temperature limit of the stochastic homogeneous Ising ferromagnet (with Glauber dynamics): the initial state is chosen uniformly at random and then each site, at rate 1, polls its four neighbors and makes sure it agrees with the majority, or tosses a fair coin in case of a tie. Among the main results (almost sure, with respect to both the process and initial state) are: clusters (maximal domains of constant sign) are finite for times t < infinity, but the cluster of a fixed site diverges (in diameter) as t --> infinity; each of the two constant states is (positive) recurrent. We also present other results and conjectures concerning positive and null recurrence and the role of absorbing states.